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We introduce a concept that uses detuned arm cavities to increase the shot-noise-limited sensitivity of LIGO without increasing the light power inside the arm cavities. Numerical simulations show an increased sensitivity between 125 and 400 Hz, with a maximal improvement of about 80% around 225 Hz, while the sensitivity above 400 Hz is decreased. Furthermore, our concept is found to give a sensitivity similar to that of a conventional RSE configuration with a signal-recycling mirror of moderate reflectivity. In the near future detuned arm cavities might be a beneficial alternative to RSE, due to the potentially less hardware-intensive implementation of the proposed concept.